Asymptotic stability of solitons for mKdV

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• 作者：Pierre Germain^a ; ^{pgermain@cims.nyu.edu" class="auth_mail" title="E-mail the corresponding author} ; Fabio Pusateri^b ; ^{fabiop@math.princeton.edu" class="auth_mail" title="E-mail the corresponding author} ; Fré ; dé ; ric Rousset^c ; ^d ; ^{frederic.rousset@math.u-psud.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：mKdV ; Modified scattering ; Asymptotic stability ; Solitons
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：20 August 2016
• 年：2016
• 卷：299
• 期：Complete
• 页码：272-330
• 全文大小：793 K

文摘

We prove a full asymptotic stability result for solitary wave solutions of the mKdV equation. We consider small perturbations of solitary waves with polynomial decay at infinity and prove that solutions of the Cauchy problem evolving from such data tend uniformly, on the real line, to another solitary wave as time goes to infinity. We describe precisely the asymptotics of the perturbation behind the solitary wave showing that it satisfies a nonlinearly modified scattering behavior. This latter part of our result relies on a precise study of the asymptotic behavior of small solutions of the mKdV equation.